Minimum Disparity Estimator in Continuous Time Stochastic Volatility Model

Abstract

In the study of finance, likelihood based or moment based methods are frequently used to estimate parameters for various kinds of models given the sampled return data. While the former method is not robust, the latter one suffers from loss of efficiency and high noise-to-signal ratio in the data. In this paper, we investigate the ergodic behavior of the bivariate series described by the Barndorff-Nielsen and Shephard (BN-S) stochastic volatility model. In particular, we study its beta-mixing property and the differentiability of its stationary distribution. A robust and efficient estimation scheme for continuous models called the Negative Exponential Disparity Estimator (NEDE) is studied. We apply this method and the classical Method of Moments (MOM) to the BN-S model. Asymptotic properties of the NEDE and the MOM estimator are proved, implementation details are provided.